Question

Prove 7√11 /3 as irrational ?

Answer 1

To prove (7√11) /3 as irrational
first we have to assume that (7√11) /3 is rational
A rational number can be expressed in terms of two coprime numbers as follows
(7√11) /3=a/b------1
a & b are coprime numbers(they do not have any common factor)
(7√11) =3a/b-------2
√11 =3a/7b

as 3 and 7 are coprime the numerator and denominator in RHS is coprime
So √11 is also rational
But we know that √11 is an irrational number.
This concludes that our assumption that (7√11) /3 is a rational number is false
so (7√11) /3 is an irrational number

hence proved